Transcranial stimulation analysis using the smoothed finite element method

Abstract

This paper presents a series of smoothed finite element methods (SFEM) for transcranial stimulation simulations. The problem domain is first discretized into a set of four-node tetrahedral elements, and linear shape functions are employed to interpolate the field variables. Then, the smoothing domains are further formed in conjunction with the nodes, edges or faces of elements. In order to improve the accuracy of low-order interpolation, the magnetic flux density and gradient of electric potential are smoothed using the gradient smoothing technique (GST) over each smoothing domain. Based on the generalized smoothed Galerkin weakform, the discretized system equations are finally obtained. Numerical examples, including transcranial direct current stimulation (tDCS) and transcranial magnetic stimulation (TMS) problems, demonstrate that the SFEM possesses the following important properties: (1) better accuracy; (2) faster convergence; (3) higher computational efficiency; (4) more robust in transcranial stimulation simulations.